curve #567

y² + xy + y = x³ − x² − 212703862469161792233542757x + 1151729957509229659893398984446400016285

a-invariants: [1, -1, 1, -212703862469161792233542757, 1151729957509229659893398984446400016285]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 73163661535123456243878232619943344816771529154713331186240511378692220654
naive height: 193.4794
Faltings height: 14.0461
discriminant (Δ): 42854005143644791778814309436014175472837954228731930049054282248818637019226112
primes of bad reduction: 2, 11, 13, 26522987521, 607709874587, 34798725286181, 358060867847516809, 1273768395850682183
regulator: 24643027586252043032993.4562547542683650837427638951354114670485341277047833461
submitted by: Jason Ma
submitted at: 2026-09-04 07:48:08 UTC
last updated: 2026-09-04 07:48:08 UTC

(-83495758694755785/6241, 19738932581529107572396056/493039)
(992050058609793153/32761, 889021646477840953841983652/5929741)
(1927549661193006080101/59706529, 77105532486575312377188583223340/461352349583)
(189886360127959276263/19123129, 361623655253260586802988972704/83625443117)
(181829011699697649698615/4635294889, 72768891118296989749305162973441888/315584781927787)
(200842364706277063407/40972801, 3950320329464766830251352810032/262266899201)
(38377618286019098007/1371241, 210106332117983655591095133600/1605723211)
(2795286689539500367/137641, 3685169084088614929763991320/51064811)
(27489214998585, 126795427316736452340)
(2580444121426337825/591361, 7963664262279779410132230026/454756609)
(-5470360005309, 46385313120687399452)
(383033228963971975/38809, -28425881987464101951623520/7645373)
(5394683216797803729823/177608929, 356728484564234197016422774104736/2366994196783)
(2829600721168691/289, 13675588993280040215180/4913)
(37707615675600139/225, 7295353725924746088833408/3375)
(-56119807363225471649/3352561, 28640889157195429190028899232/6138539191)
(1874293364193204001075/38266596, 77878743080980577837150770344085/236717162856)
(179031438512923/4, 2280960442427781828285/8)
(55653661507311191/42025, 254455404830282840522704096/8615125)
(6285765191179227049/59049, 15618295096828937178729080732/14348907)

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